Instructor: Cecilia Flori, Perimeter Institute
Type: Perimeter Institute non-credit mini-course
Dates: April 29, May 3 and 6, 2011; 2:30 pm, Bob Room

In this mini-course I will first introduce the notion of a topos describing, in general terms, what a topos is and how it can be used as an alternative mathematical universe. I will then delineate, through examples, how Topos Theory can be used in physics. In particular, I will focus on how Quantum Theory can be described in terms of Topos Theory. The advantage of such a reformulation of Quantum Theory rests on the fact that it overcomes certain interpretational problems present in the Copenhagen interpretation, namely the topos approach offers a more realist interpretation of Quantum Theory as opposed to the standard instrumentalist interpretation. This is achieved by proposing a radical new way of thinking about a theory of physics. In this new perspective, the underlining structure is a logical structure in which probabilities are replaced by truth values, i.e logical concepts are seen as fundamental, while probabilities become derived concepts.